Medium4 marksStructured
AQA GCSE · Question 09.1 · Probability
A number is picked at random from the first three positive odd numbers.
A number is picked at random from the first four prime numbers.
The two numbers are multiplied to get a score.
Complete the table.
A number is picked at random from the first three positive odd numbers.
A number is picked at random from the first four prime numbers.
The two numbers are multiplied to get a score.
Complete the table.
How to approach this question
1. **Identify the numbers:**
- First three positive odd numbers: 1, 3, 5. The table already has 1 and 5, so the missing odd number is 3.
- First four prime numbers: 2, 3, 5, 7. The table has 2, 3, and 7, so the missing prime number is 5.
2. **Fill in the missing headers:**
- The missing odd number in the first column is 3.
- The missing prime number in the top row is 5 (it should go between 3 and 7).
3. **Complete the multiplication:**
- Row 1 (odd number 1): 1×2=2, 1×3=3, 1×5=5, 1×7=7.
- Row 2 (odd number 3): 3×2=6, 3×3=9, 3×5=15, 3×7=21.
- Row 3 (odd number 5): 5×2=10, 5×3=15, 5×5=25, 5×7=35.
Full Answer
This question requires us to complete a sample space diagram for a probability problem.
**Step 1: Identify the sets of numbers.**
- The first three positive odd numbers are 1, 3, 5. The table shows 1 and 5, so the missing odd number is 3.
- The first four prime numbers are 2, 3, 5, 7. (A prime number is a number greater than 1 that has only two factors: 1 and itself). The table shows 2, 3, and 7, so the missing prime number is 5.
**Step 2: Fill in the table by multiplying.**
The table shows the result of multiplying the odd number in the row by the prime number in the column.
- **Top row (multiplying by 1):** 1×2=2, 1×3=3, 1×5=5, 1×7=7.
- **Middle row (multiplying by 3):** 3×2=6, 3×3=9, 3×5=15, 3×7=21.
- **Bottom row (multiplying by 5):** 5×2=10, 5×3=15, 5×5=25, 5×7=35.
The value 15 is already given as a check.
Common mistakes
✗ Incorrectly identifying the odd or prime numbers (e.g., thinking 1 is a prime number, or 9 is a prime number).\n✗ Making multiplication errors when filling the table.
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